Human Calculator

Below is a table of perfect cubes from 1 to a million. If someone gives you one of these numbers at random, can you calculate the cube root in your head?

1	1,331	9,261	29,791	68,921	132,651	226,981	357,911	531,441	753,571
8	1,728	10,648	32,768	74,088	140,608	238,328	373,248	551,368	778,688
27	2,197	12,167	35,937	79,507	148,877	250,047	389,017	571,787	804,357
64	2,744	13,824	39,304	85,184	157,464	262,144	405,224	592,704	830,584
125	3,375	15,625	42,875	91,125	166,375	274,625	421,875	614,125	857,375
216	4,096	17,576	46,656	97,336	175,616	287,496	438,976	636,056	884,736
343	4,913	19,683	50,653	103,823	185,193	300,763	456,533	658,503	912,673
512	5,832	21,952	54,872	110,592	195,112	314,432	474,552	681,472	941,192
729	6,859	24,389	59,319	117,649	205,379	328,509	493,039	704,969	970,299
1,000	8,000	27,000	64,000	125,000	216,000	343,000	512,000	729,000	1,000,000

For example, what is the cube root of 681,472 ?
You wouldn't have the table in front of you so you can't find the position of the number in the table

Actually if you can do this you would be sort of a human mini calculator, still far below Shakuntla Devi , a poor woman from India.








Now try it again. What is the cube root of 148,877 ?

What have you got to lose?

to solve the 23rd root, she would have been presented with :

916748676920039158098660927585380162483106680144308622407126516427934657040867096593279205767480806790022783016354924852380335745316935111903596577547340075681688305620821016129132845564805780158806771

she was better than my online calculator, which uses logarithms I assume. It came up with 546372890.9999996 as the answer , assuming that the above number is what was given to her

Holy cow!*

*no kidding, it just occurred to me that to say 'holy cow' might be very offensive to such a person, if she is Hindu. Is it possible that I summoned that up unconsciously? sorry for hijacking but I just had to ponder that

Quote: odiousgambit

she was better than my online calculator, which uses logarithms I assume.

Yes, all calculators use logarithms to base 2.

In 1988 Shakuntala did the cube root of 95,443,993 in 2 seconds. She died in 2013 and received a Google Doodle.


450 91,125,000
451 91,733,851
452 92,345,408
453 92,959,677
454 93,576,664
455 94,196,375
456 94,818,816
457 95,443,993 ----------------------
458 96,071,912
459 96,702,579

It is actually possible for a normal person to do the cube roots of perfect cubes up to a million in 2 seconds, although you may want to draw it out as party trick.